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6 Forecasting Crime: A City-Level Analysis--John V. Pepper
Pages 177-210

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From page 177...
... My more modest objective is to examine whether historical timeseries data can be used to provide accurate forecasts of future crime rates. To do this, I analyze forecasts from a number of basic and parsimoniously specified mean regression models.
From page 178...
... Most importantly, I contrast the homogeneous panel data model with heterogeneous models in which the process can vary arbitrarily across cities. I also consider two naïve models, one in which the forecast simply equals the city-level mean or fixed effect -- the best constant forecast -- and the other in which the forecast equals the last observed rate -- a random walk forecast.
From page 179...
... A naïve random walk forecasting model performs quite well for shorter run forecast horizons, but the regression models are superior for longer horizon forecasts. Finally, I use the basic homogeneous panel data models to provide point forecasts for city-level crime rates in 2005, 2006, and 2009.
From page 180...
... that is incarcerated. Figure 6-2 displays the time series for these two random variables along with the homicide rate series. All three series are normalized to be relative to a 1935 base.
From page 181...
... I follow the convention in the literature by taking the natural logarithm of the crime and incarceration rates. I estimate the regression models using the annual data for 1935-2000, leaving out pre-1935 data because accurate homicide rate and covariate information is not readily available, and the post-2000 data to assess forecasting performance.
From page 182...
... Consistent with Figure 6-1, there is a strong autoregressive component to the series, with the period t homicide rate being strongly associated with the lagged rates. In the unrestricted Model C, the regression coefficients associated with the incarceration rate are positive, small, and statistically insignificant.
From page 183...
... In particular, the model forecasts a steady drop in homicide rates throughout the 1980s, yet the actual rates rose in the late 1980s. Ultimately, the ability of this model to effectively forecast crime depends on observed relationships continuing into future periods.
From page 184...
... 184 UNDERSTANDING CRIME TRENDS A 2.4 2.2 Log-Homicide Rate 2.0 1.8 1970 1980 1990 2000 Year Log-Homicide Rate Model A Forecasts: Lag Only Model B Forecasts: Full Model B 2.4 Figure 6-3a, editable 2.2 Log-Homicide Rate 2.0 1.8 1970 1980 1990 2000 Year Log-Homicide Rate Model A Forecasts: Lag Only Model B Forecasts: Full Model FIGURE 6-3  Realized and forecasted homicide rates. Figure 6-3b, editable
From page 185...
... FORECASTING CRIME 185 C 2.4 2.2 Log-Homicide Rate 2.0 1.8 1970 1980 1990 2000 Year Log-Homicide Rate Model A Forecasts: Lag Only Model B Forecasts: Full Model D 2.4 Figure 6-3c, editable Log-Homicide Rate 2.2 2.0 1.8 1970 1980 1990 2000 Year Log-Homicide Rate Model A Forecasts: Lag Only Model B Forecasts: Full Model FIGURE 6-3  Continued Figure 6-3d, editable
From page 186...
... Finally, during this 23-year period, the forecasting models consistently underpredict during the period from 1989 to 1994 and overpredict homicide rates after 1995.
From page 187...
... Both models predict relatively modest changes to the homicide rate over the period, yet they have different qualitative implications. The Model A forecasts imply that homicide rates will continue to fall during the period, whereas the Model C forecasts suggest that homicide rates will increase.
From page 188...
... TABLE 6-3  Two- and Five-Year-Ahead Forecasts of National Log-Homicide Rates, 1980-2002 188 Two-Year-Ahead Forecasts Five-Year-Ahead Forecasts Model A Model C Naïve Model Model A Model C Naïve Model Year Log Forecast Error Forecast Error Forecast Error Forecast Error Forecast Error Forecast Error 1980 2.37 2.17 –0.20 2.23 –0.14 2.22 –0.15 2.10 –0.27 2.28 –0.09 2.29 –0.08 1981 2.33 2.28 –0.06 2.31 –0.02 2.30 –0.03 2.02 –0.31 2.21 –0.12 2.20 –0.13 1982 2.26 2.32 0.06 2.36 0.10 2.37 0.11 2.08 –0.19 2.23 –0.03 2.21 –0.05 1983 2.15 2.23 0.08 2.30 0.15 2.33 0.18 2.08 –0.07 2.22 0.07 2.22 0.07 1984 2.13 2.16 0.03 2.23 0.10 2.26 0.13 2.15 0.03 2.28 0.15 2.30 0.17 1985 2.13 2.05 –0.08 2.12 –0.01 2.15 0.02 2.18 0.05 2.30 0.17 2.37 0.24 1986 2.20 2.08 –0.12 2.01 –0.10 2.13 –0.07 2.11 –0.08 2.23 0.03 2.33 0.13 1987 2.16 2.09 –0.07 2.09 –0.08 2.13 –0.04 2.06 –0.10 2.15 –0.01 2.26 0.10 1988 2.20 2.18 –0.01 2.15 –0.05 2.20 0.00 1.99 –0.20 2.05 –0.15 2.15 –0.05 1989 2.23 2.10 –0.13 2.01 –0.13 2.16 –0.07 2.02 –0.21 2.02 –0.21 2.13 –0.10 1990 2.30 2.16 –0.14 2.14 –0.16 2.20 –0.11 2.03 –0.27 2.01 –0.29 2.13 –0.17 1991 2.35 2.19 –0.16 2.18 –0.17 2.23 –0.12 2.01 –0.26 2.07 –0.28 2.20 –0.15 1992 2.30 2.27 –0.03 2.24 –0.06 2.30 0.00 2.03 –0.27 2.03 –0.27 2.16 –0.14 1993 2.31 2.30 –0.02 2.26 –0.05 2.35 0.04 2.08 –0.23 2.05 –0.26 2.20 –0.12 1994 2.26 2.20 –0.06 2.18 –0.08 2.30 0.04 2.01 –0.17 2.05 –0.21 2.23 –0.03 1995 2.16 2.24 0.08 2.20 0.04 2.31 0.15 2.15 –0.01 2.09 –0.08 2.30 0.14 1996 2.07 2.17 0.10 2.15 0.08 2.26 0.19 2.16 0.01 2.09 0.02 2.35 0.28 1997 2.00 2.07 0.06 2.06 0.06 2.16 0.16 2.09 0.09 2.04 0.04 2.30 0.30 1998 1.92 1.99 0.07 1.98 0.06 2.07 0.15 2.13 0.21 2.06 0.14 2.31 0.40 1999 1.82 1.95 0.13 1.94 0.11 2.00 0.18 2.07 0.25 2.02 0.20 2.26 0.44 2000 1.81 1.87 0.07 1.87 0.06 1.92 0.11 2.00 0.20 1.96 0.16 2.16 0.36 2001 1.96 1.80 –0.16 1.79 –0.17 1.82 –0.14 1.96 –0.00 1.92 –0.04 2.07 0.11 2002 1.81 1.82 0.02 1.79 –0.01 1.81 0.00 1.94 0.13 1.89 0.08 2.00 0.19 Mean 2.14 2.12 2.12 2.17 2.07 2.10 2.22
From page 189...
... terms and the covariates. The naïve model simply forecasts crime as the last observed crime rate, a random walk forecast.
From page 190...
... I then assess forecast performance of these models to 1-, 2-, 4-, and 10-year-ahead forecasts of city-level crime rates. I compare the performance of a basic homogeneous panel data regression model with a flexible heterogeneous alternative.
From page 191...
... As with the forecasted national homicide rate series, I find the qualitative predictions are sensitive to the underlying model. Best Linear Predictor To forecast city-level crime rates, I begin by considering the following dynamic panel data model: yit = γ i yi, t −1 + xi, t − 2 β + ν i + ε it , , (2)
From page 192...
... (0.046) RMSE 0.306 0.315 0.296 0.181 0.238 0.177 0.158 0.188 0.149 0.188 0.287 0.186 R2 0.846 0.833 0.852 0.940 0.892 0.940 0.884 0.844 0.902 0.916 0.797 0.915 N 1963 1586 1572 1980 1594 1585 1980 1594 1585 1980 1594 1585 NOTE: All regressions include city-level fixed effects.
From page 193...
... Variation in the slope parameters across the cross-sectional units may compromise the ability of the homogeneous dynamic panel data model in Equation (2) to accurately forecast crime rates.
From page 194...
... [0.805, 0.919] Median 0.567 0.798 0.963 0.861 Mean 0.486 0.752 0.902 0.822 Minimum –0.585 0.023 0.029 –0.021 Maximum 1.059 1.129 1.371 1.117 Homogeneous model 0.452 0.759 0.923 0.851 TABLE 6-7  Heterogeneous Model Coefficient Estimates for Selected Cities Homicide Robbery Burglary MVT Denver 0.63 0.94 1.02 0.68 Knoxville –0.03 0.76 1.01 0.73 Madison 0.25 0.65 0.95 0.93 New York 1.06 1.13 1.07 1.12 Richmond 0.76 0.73 0.90 0.67 San Francisco 0.73 0.94 0.94 0.95 the IQR has a width of 0.18 for burglary and a width of 0.11 for motor vehicle theft.
From page 195...
... In-Sample Forecasts How well does the homogeneous panel data model do at forecasting crime rates? Given my focus on two-period-ahead forecasts, I begin by using this model to predict the 2003 and 2004 crimes rates for each city.
From page 196...
... TABLE 6-8  Homogeneous Model Forecasts for Selected Cities, 2003-2004 196 2003 2004 Model A Model C Model A Model C y Forecast Error Forecast Error y Forecast Error Forecast Error Homicide Denver 2.41 2.40 –0.01 2.35 –0.06 2.73 2.50 –0.23 2.42 –0.32 Knoxville 2.33 2.54 0.21 2.27 –0.06 2.43 2.56 0.12 2.21 –0.23 Madison 1.31 0.51 –0.80 0.27 –1.04 0.34 0.59 0.25 0.23 –0.10 New York 2.00 2.49 0.48 2.46 0.46 1.95 2.71 0.77 2.60 0.66 Richmond 3.83 3.76 –0.07 3.62 –0.21 3.86 3.78 –0.08 3.60 –0.26 San Francisco 2.19 2.30 0.12 2.31 0.12 2.45 2.38 –0.07 2.37 –0.08 Robbery Denver 5.53 5.39 –0.14 5.43 –0.10 5.54 5.44 –0.11 5.50 –0.05 Knoxville 5.54 5.74 0.20 5.63 0.09 5.69 5.74 0.04 5.56 –0.13 Madison 4.86 4.84 –0.01 4.69 –0.16 4.89 4.85 –0.04 4.59 –0.30 New York 5.77 6.03 0.26 6.04 0.27 5.71 6.19 0.48 6.18 0.48 Richmond 6.38 6.45 0.07 6.30 –0.08 6.53 6.45 –0.08 6.20 –0.32 San Francisco 5.98 6.11 0.13 6.19 0.20 5.99 6.20 0.21 6.33 0.33 Burglary Denver 7.13 6.94 –0.19 7.01 –0.04 7.17 6.92 –0.25 7.19 0.02 Knoxville 7.20 7.08 –0.12 6.99 –0.21 7.27 7.07 –0.20 6.93 –0.34 Madison 6.61 6.58 –0.03 6.49 –0.12 6.49 6.55 0.06 6.42 –0.07 New York 5.86 5.93 0.08 6.17 0.31 5.78 5.95 0.17 6.32 0.54 Richmond 7.25 7.30 0.04 7.25 0.00 7.24 7.30 0.06 7.23 –0.01 San Francisco 6.62 6.60 –0.02 6.71 0.09 6.69 6.59 –0.10 6.78 0.01 MVT Denver 7.14 7.13 –0.01 7.14 0.01 7.20 7.11 –0.09 7.14 –0.06 Knoxville 6.69 6.57 –0.12 6.51 –0.19 6.67 6.61 –0.06 6.49 –0.18 Madison 5.67 5.71 0.04 5.57 –0.10 5.54 5.73 0.19 5.47 –0.07 New York 5.68 5.95 0.28 6.02 0.34 5.56 6.07 0.51 6.16 0.60 Richmond 7.21 7.11 –0.11 6.91 –0.30 7.01 7.01 –0.00 6.75 –0.35 San Francisco 6.81 6.67 –0.13 6.76 –0.05 6.97 6.70 –0.27 6.85 –0.11
From page 197...
... For these one- and two-year-ahead predictions, the naïve random walk forecasts seem to be at least as accurate as the regression model forecasts. In other words, for shorter run forecasts, the basic panel data models do no
From page 198...
... The one-step-ahead predictions from the heterogeneous model for each year from 1982 to 2000 are also displayed. These in-sample predictions nearly match the realized crime rates; the heterogeneous model closely fits the observed data.
From page 199...
... FORECASTING CRIME 199 6.0 5.8 Log-Robbery Rate 5.6 5.4 5.2 1985 1990 1995 2000 2005 Year Log-Robbery Rate Homogenous Model Forecasts Heterogeneous Model Forecasts FIGURE 6-5a  Realized and forecasted log-robbery rates, Denver. 6.5 Figure 6-5a, editable 6.0 Log-Robbery Rate 5.5 5 1985 1990 1995 2000 2005 Year Log-Robbery Rate Homogenous Model Forecasts Heterogeneous Model Forecasts FIGURE 6-5b  Realized and forecasted log-robbery rates, Knoxville.
From page 200...
... 200 UNDERSTANDING CRIME TRENDS 5.2 5.0 Log-Robbery Rate 4.8 4.6 4.4 1985 1990 1995 2000 2005 Year Log-Robbery Rate Homogenous Model Forecasts Heterogeneous Model Forecasts FIGURE 6-5c  Realized and forecasted log-robbery rates, Madison. 7.5 Figure 6.5c 7.0 Log-Robbery Rate 6.5 6.0 5.5 5.0 1985 1990 1995 2000 2005 Year Log-Robbery Rate Homogenous Model Forecasts Heterogeneous Model Forecasts FIGURE 6-5d  Realized and forecasted log-robbery rates, New York.
From page 201...
... FORECASTING CRIME 201 6.6 6.5 Log-Robbery Rate 6.4 6.3 6.2 6.1 1985 1990 1995 2000 2005 Year Log-Robbery Rate Homogenous Model Forecasts Heterogeneous Model Forecasts FIGURE 6-5e  Realized and forecasted log-robbery rates, Richmond. Figure 6-5e, editable 7.0 Log-Robbery Rate 6.5 6.0 1985 1990 1995 2000 2005 Year Log-Robbery Rate Homogenous Model Forecasts Heterogeneous Model Forecasts FIGURE 6-5f  Realized and forecasted log-robbery rates, San Francisco.
From page 202...
... Many of the findings reported in this table confirm the earlier results. In particular, for shorter run forecasts, the restricted Model A seems to do at least as well as the unrestricted Model C, and both of these homogeneous models provide slightly less accurate forecasts than the naïve random walk model.
From page 203...
... This is the one step-ahead forecast. Naïve Forecast equals the crime rate in the "last observed" year, namely 2002, 2000, and 1995.
From page 204...
... In San Francisco, log-robbery rates are forecasted to increase by 0.38 points, whereas forecasts for the other three crime rates are slightly less than the 2004 levels. In Madison, log-homicide rates are forecasted to increase by 0.31 and log-MVT rates by 0.15, whereas the log-crime rates for both robbery and burglary are forecasted to drop over the same period.
From page 205...
... The results in this table confirm that Models A and C provide different pictures about what to expect for crime in large cities over this period. Forecasts made using Model A generally imply modest increases (e.g., homicide)
From page 206...
... [0.04, 0.37] Mean absolute change 0.08 0.09 0.13 0.15 0.23 Burglary Mean forecast 6.99 6.99 6.91 6.99 6.88 6.99 Mean change from 2004 0.00 –0.06 0.00 –0.09 0.00 Fraction positive change 0.54 0.28 0.54 0.28 0.54 IQR [–0.01, 0.01]
From page 207...
... Yet these results also reveal that, for short-run forecasts, the naïve random walk model provides slightly more accurate forecasts than either panel data model. That is, for these shortrun forecasts, one might not be able to do better than the predicting that tomorrow will look like today.
From page 208...
... . ACKNOWLEDGMENTS I have benefited from the comments of Phil Cook, Richard Rosenfeld, Jose Fernandez, Elizabeth Wittner, several anonymous referees, the University of Virginia Public Economics Lunch Group, and participants at the Committee on Law and Justice Workshop on Understanding Crime Trends.
From page 209...
... . The indeterminacy of forecasts of crime rates and juvenile offenses.


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